Transcript Gravity (Chap. 9)

Chapter 9
Gravity
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Newton and the Moon
Newton realized that
Earth’s gravity was
the centripetal force
that kept the moon in
orbit.
Also discovered that
gravity was weaker at
that great distance.
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Gravity
force
Gravity & Distance
We don’t notice that
gravity gets
weaker as we
move away from
Earth because we
rarely go very far.
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Universal Law of Gravity
Force of gravity has magnitude given by
(Gravity Force) = (G) x
( Mass of Object A ) x ( Mass of Object B)
( Distance ) x ( Distance )
DISTANCE
Object
A
Force
Force
Equal and opposite forces
(Newton’s Third law)
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Object
B
Universal Gravity Constant, G
In the formula for gravity force, we have
G = 0.0000000000667 N m2 / kg2
= 6.67 x 10–11 N m2 / kg2
The formula and the constant are called
“universal” because, up to now, this theory
predicts gravity anywhere in the universe.
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Cavendish Experiment
For non-astronomical
objects gravity force
is very small.
Need sensitive balance
to detect.
First measured by
Cavendish in his
home laboratory in
1797 at age 67.
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“Intelligent Falling”
Universal Law of Gravity
"Things fall not
because they are
acted upon by
some gravitational
force, but because
a higher
intelligence, 'God' if
you will, is pushing
them down,"
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The Onion, August 17, 2005
Sample Problem
Here is an example of using the formula
(Gravity Force) = (G) x
( Mass of Object A ) x ( Mass of Object B)
( Distance ) x ( Distance )
Object A (1 kg mass)
Force
Object B (Earth)
DISTANCE = Earth’s Radius
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Sample Problem
Find gravity force for a 1 kg mass on surface
of Earth.
Earth’s Mass
(Force) = (6.67 x 10–11) x
( 1 ) x ( 6 x 1024 )
( 6.38 x 106 )2
Universal Gravity Constant, G
Earth’s Radius
Value comes out to 9.8 Newtons (check this
with your calculator; it’s good practice).
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Sample Problem (cont.)
Find gravity acceleration on a 1 kg mass.
Using Newton’s Second Law,
(Acceleration) =
( 9.8 N )
(Force)
=
(1 kg )
(Mass)
Answer is 9.8 m/s2, which we’ve been
rounding off as 10 m/s2.
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Inverse Square Law
Gravity force
weakens with
distance as the
inverse of the
square of the
distance.
Geometric
property of
area and
distance.
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1/4 Earth Gravity
Earth Gravity
Outer circle is twice Earth’s radius
so it has 4 times the area
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Demo: Perspective
These four
figures are
equally
spaced in
distance and,
in perspective,
you are
standing that
distance from
the first.
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At twice the distance,
the face is ¼ the size.
At four
times
the
distance
face is
16th the
size.
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Demo: Perspective Cards
Hold large card at arm’s
length.
Close one eye then hold
small card at a distance
such that it is same size
as large card.
That distance will be half
way between your eye
and large card.
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1
2
3
4
1
Arm’s length
Half
Weightlessness
In deep space, far away
from all stars, planets,
etc. there is almost no
gravity force.
In orbit near Earth, gravity
is still strong (only 10%
less than on surface).
Why are Shuttle and
Space Station
astronauts
“weightless”?
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Earth is nearby
Freefall & Weightlessness
Freefall is a state of weightlessness, even though gravity is present.
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Movie: Roller Coaster
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Check Yourself
Sit in a seat on Ferris
wheel.
Where do you feel
heaviest?
A
B
C
Where do you feel
lightest?
Centripetal
Force
E
Velocity
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D
Demo: Ferris Wheel in Hand
Place a heavy object
in your hand, hold
your arm out and
rotate your arm,
palm upward, in a
small circle.
Object will feel
lightest at the top
of the circle and
heaviest at bottom.
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Support
Force
Support
Force
Demo: Falling Slinky
Hold a Slinky and its
weight stretches it
out.
Now drop it.
In freefall it’s in a state
of weightlessness so
Slinky immediately
contracts.
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NASA’s “Vomit Comet”
NASA has a special
airplane for training
astronauts in freefall weightless
conditions.
The “Vomit Comet”
nickname tells you
it’s quite a wild
roller-coaster ride.
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The plane flies between 20,000 and
30,000 feet, same as commercial flights.
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Flight of the “Vomit Comet”
At the top of
the arc, the
plane’s
trajectory is
projectile
motion.
Weightless
Freefall
Boeing 707 (modified)
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